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Discontinuity-induced intermittent synchronization transitions in coupled non-smooth systems
Ming Yi1, Canjun Wang2, Keli Yang2
1School of Mathematics and Physics, China University of Geosciences, Wuhan 430074, China.
Synchronization in coupled non-smooth systems transitions intermittently between cluster and complete states. Discontinuities and coupling strength significantly influence this transition and the emergence of periodic clusters.
Area of Science:
- Nonlinear Dynamics
- Complex Systems
- Chaos Theory
Background:
- Coupled non-smooth systems are prevalent in various scientific domains.
- Understanding synchronization transitions is crucial for analyzing system behavior.
- Previous studies have explored synchronization in smooth systems, but non-smooth aspects remain less understood.
Purpose of the Study:
- To investigate the synchronization transition in coupled non-smooth systems.
- To analyze the impact of coupling strength and initial conditions on synchronization.
- To elucidate the role of discontinuities in the synchronization dynamics.
Main Methods:
- Numerical simulations were employed to study the system dynamics.
- The average order parameter was calculated to quantify synchronization.
- Phase space analysis was used to characterize periodic cluster states.
Main Results:
- An intermittent synchronization transition was observed, shifting from cluster to complete synchronization.
- Discontinuities were identified as critical factors influencing the synchronization transition.
- Increasing coupling strength promoted the coexistence of multiple periodic cluster states.
Conclusions:
- The study highlights the significant role of non-smoothness in synchronization phenomena.
- Periodic clusters arise from the interplay of nonlinearity and coupling across discontinuous boundaries.
- The findings offer insights into the complex dynamics of coupled non-smooth systems.
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